Reference. Reference. Properties of Equality. Properties of Segment and Angle Congruence. Other Properties. Triangle Inequalities

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1 Refeene opeties opeties of qulity ddition opety of qulity If =, ten + = +. Multiplition opety of qulity If =, ten =, 0. Reflexive opety of qulity = Tnsitive opety of qulity If = nd =, ten =. Suttion opety of qulity If =, ten =. ivision opety of qulity If =, ten =, 0. Symmeti opety of qulity If =, ten =. Sustitution opety of qulity If =, ten n e sustituted fo (o fo ) in ny eqution o expession. opeties of Segment nd ngle onguene Reflexive opety of onguene Fo ny segment,. Symmeti opety of onguene If, ten. Tnsitive opety of onguene If nd F, ten F. Ote opeties Tnsitive opety of llel Lines If p q nd q, ten p. Fo ny ngle,. If, ten. If nd, ten. Refeene istiutive opety Sum ( + ) = + iffeene ( ) = Tingle Inequlities Tingle Inequlity Teoem ytgoen Inequlities Teoem + > + > + > If < +, ten is ute. If > +, ten is otuse. Refeene 05

2 Fomuls oodinte Geomety Slope m = y y x x Slope-inteept fom y = mx + oint-slope fom y y = m(x x ) Midpoint Fomul ( x + x, y + y ) Stndd fom of line eqution x + y = olygons Tingle Sum Teoem istne Fomul d = ( x x ) + ( y y ) Stndd eqution of ile (x ) + (y k) =, wit ente (, k) nd dius xteio ngle Teoem titioning segment on nume line x + x ptitions te segment in + te tio :. m + m + m = 80 Tingle Midsegment Teoem m = m + m Tpezoid Midsegment Teoem M N, = MN, MN, MN = ( + ) olygon Inteio ngles Teoem olygon xteio ngles Teoem n = m + m m n = (n ) 80 Geometi Men (ltitude) Teoem n = 5 m + m m n = 360 Geometi Men (Leg) Teoem = = = 06 Refeene

3 Rigt Tingles ytgoen Teoem + = Tigonomety Tingles x 45 x 45 x ypotenuse = leg Tingles 60 x x 30 x 3 ypotenuse = sote leg longe leg = sote leg 3 Rtios sin = os = tn = sin = m os = m tn = m Sine nd osine of omplementy ngles Let nd e omplementy ngles. Ten te following sttements e tue. sin = os(90 ) = os sin = os(90 ) = os os = sin(90 ) = sin os = sin(90 ) = os ny Tingle onvesion etween degees nd dins 80 = π dins Refeene e e = sin e = sin e = sin Lw of Sines sin sin = = sin = sin sin = sin Lw of osines = + os = + os = + os oility nd omintois Nume of fvole outomes Teoetil oility = Totl nume of outomes oility of te omplement of n event ( ) = () oility of dependent events ( nd ) = () ( ) Nume of suesses xpeimentl oility = Nume of tils oility of independent events ( nd ) = () () oility of ompound events ( o ) = () + () ( nd ) emuttions n = n! (n )! omintions n = n! (n )!! inomil expeiments (k suesses) = n k p k ( p) n k Refeene 07

4 iles lengt lengt of = m 360 π e of seto e of seto = m 360 π entl ngles m = m Insied ngles m = m Tngent nd inteseted od m = m m = m ngles nd Segments of iles Two ods m = ( m + m ) = Tngent nd sent m = ( m m ) = Two sents m = ( m m ) = Two tngents m = ( m m ) = 08 Refeene

5 eimete, e, nd Volume Fomuls Sque Retngle Tingle s w s = 4s = s ile = + w = w llelogm = + + = Tpezoid d = πd o = π = π Romus/Kite = Regul n-gon = ( + ) Speil tingle d d s Refeene d = d d d = o = ns = π (m + m + m 80 ) 80 ism ylinde ymid L = S = + V = L = π S = π + π V = π L = S = + V = 3 one L = π Spee S = 4π S = π + π V = 3 π V = 4 3 π3 Refeene 09

6 Ote Fomuls Geometi men x = Qudti Fomul x = ± 4, wee 0 nd 4 0 Simil polygons o simil solids wit sle fto : Rtio of peimetes = : Rtio of es = : Rtio of volumes = 3 : 3 onvesions U.S. ustomy foot = ines yd = 3 feet mile = 580 feet mile = 760 yds e = 43,560 sque feet up = 8 fluid ounes pint = ups qut = pints gllon = 4 quts gllon = 3 ui ines pound = 6 ounes ton = 000 pounds U.S. ustomy to Meti in =.54 entimetes foot 0.3 mete mile.6 kilometes qut 0.95 lite gllon 3.79 lites up 37 millilites pound 0.45 kilogm oune 8.3 gms gllon 3785 ui entimetes Time minute = 60 seonds ou = 60 minutes ou = 3600 seonds ye = 5 weeks Tempetue = 5 (F 3) 9 F = Meti entimete = 0 millimetes mete = 00 entimetes kilomete = 000 metes lite = 000 millilites kilolite = 000 lites millilite = ui entimete lite = 000 ui entimetes ui millimete = 0.00 millilite gm = 000 milligms kilogm = 000 gms Meti to U.S. ustomy entimete 0.39 in mete 3.8 feet mete ines kilomete 0.6 mile lite.06 quts lite 0.6 gllon kilogm. pounds gm oune ui mete 64 gllons 0 Refeene